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<h2 class="hd hd-2 unit-title">1. Syllabus and Schedule</h2>
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<h2>Syllabus and Schedule</h2>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Getting started</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Released: 7 August</h4>
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<td style="text-align: left;" rowspan="6"><span style="color: #27408c;"><b class="bf">Overview and logistics</b></span></td>
<td style="text-align: left;">Meet the course team</td>
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<td style="text-align: left;">Course description</td>
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<td style="text-align: left;">Prerequisites and resources</td>
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<td style="text-align: left;">Syllabus</td>
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<td style="text-align: left;">Grading and certification</td>
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<td style="text-align: left;">Discussion forum</td>
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<td style="text-align: left;" rowspan="3"><span style="color: #27408c;"><b class="bf">Tutorial on using the edX platform</b></span></td>
<td style="text-align: left;">Navigating courseware</td>
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<td style="text-align: left;">Interactive problems</td>
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<td style="text-align: left;">Discussion forum</td>
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<td style="text-align: left;" rowspan="3"><span style="color: #27408c;"><b class="bf">Choose your calculus adventure</b></span></td>
<td style="text-align: left;">How to succeed in this course</td>
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<td style="text-align: left;">Diagnostics</td>
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<td style="text-align: left;">Plan your path through course</td>
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<p class="hideshowbottom" onclick="hideshow(this);"><a>Show</a></p>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Unit 0: Limits</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Released: 7 August</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">(Optional)</h4>
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<td style="text-align: left;" rowspan="4"><span style="color: #27408c;"><b class="bf">Introduction to limits</b></span></td>
<td style="text-align: left;">Right- and left-hand limits</td>
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<td style="text-align: left;">When limits do not exist</td>
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<td style="text-align: left;">Graphical limits</td>
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<td style="text-align: left;">Limit laws</td>
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<td style="text-align: left;" rowspan="4"><span style="color: #27408c;"><b class="bf">Continuity</b></span></td>
<td style="text-align: left;">Right- and left-continuity</td>
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<td style="text-align: left;">Continuous functions</td>
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<td style="text-align: left;">Jump and removable discontinuities</td>
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<td style="text-align: left;">Intermediate Value Theorem</td>
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<td style="text-align: left;" rowspan="2"><span style="color: #27408c;"><b class="bf">Limits of quotients</b></span></td>
<td style="text-align: left;">When the denominator approaches zero</td>
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<td style="text-align: left;">Infinite limits</td>
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<p class="hideshowbottom" onclick="hideshow(this);"><a>Show</a></p>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Unit 1: Introducing the derivative</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Released: 7 August</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Due: 28 August</h4>
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<td style="text-align: left;" rowspan="3"><span style="color: #27408c;"><b class="bf">What is the derivative?</b></span></td>
<td style="text-align: left;">Average rate of change</td>
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<td style="text-align: left;">Instantaneous rate of change</td>
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<td style="text-align: left;">Limit definition of derivative</td>
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<td style="text-align: left;" rowspan="3"><span style="color: #27408c;"><b class="bf">Geometric interpretation of the derivative</b></span></td>
<td style="text-align: left;">Slopes of tangent lines</td>
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<td style="text-align: left;">Secant lines</td>
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<td style="text-align: left;">Approximating derivatives graphically</td>
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<td style="text-align: left;" rowspan="2"><span style="color: #27408c;"><b class="bf">The derivative as a function</b></span></td>
<td style="text-align: left;">Where a function is increasing and decreasing</td>
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<td style="text-align: left;">Concavity</td>
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<td style="text-align: left;"><span style="color: #27408c;"><b class="bf">Calculating derivatives</b></span></td>
<td style="text-align: left;">Power rule</td>
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<td style="text-align: left;"><span style="color: #27408c;"><b class="bf">Leibniz notation</b></span></td>
<td style="text-align: left;">Notation and interpretation of units</td>
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<td style="text-align: left;" rowspan="2"><span style="color: #27408c;"><b class="bf">Second derivatives and higher</b></span></td>
<td style="text-align: left;">Derivatives of derivatives</td>
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<td style="text-align: left;">Acceleration</td>
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<td style="text-align: left;" rowspan="2"><span style="color: #27408c;"><b class="bf">Trigonometric functions:</b></span></td>
<td style="text-align: left;">Derivatives of sine and cosine</td>
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<td style="text-align: left;">Modeling oscillations</td>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Unit 2: Differentiation</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Released: 7 August</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Due: 18 September</h4>
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<td style="text-align: left;" rowspan="2"><span style="color: #27408c;"><b class="bf">Linear approximation</b></span></td>
<td style="text-align: left;">Tangent line approximation</td>
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<td style="text-align: left;">Concavity and error</td>
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<td style="text-align: left;"><span style="color: #27408c;"><b class="bf">Product rule</b></span></td>
<td style="text-align: left;">Derivatives of products of functions</td>
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<td style="text-align: left;"><span style="color: #27408c;"><b class="bf">Quotient rule</b></span></td>
<td style="text-align: left;">Derivatives of quotients of functions</td>
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<td style="text-align: left;"><span style="color: #27408c;"><b class="bf">Chain rule</b></span></td>
<td style="text-align: left;">Derivatives of compositions of functions</td>
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<td style="text-align: left;"><span style="color: #27408c;"><b class="bf">Implicit differentiation</b></span></td>
<td style="text-align: left;">Derivatives of implicitly defined functions</td>
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<td style="text-align: left;" rowspan="3"><span style="color: #27408c;"><b class="bf">Inverse functions</b></span></td>
<td style="text-align: left;">Graphing inverse functions</td>
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<td style="text-align: left;">Restricted domains</td>
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<td style="text-align: left;">Derivatives of inverses</td>
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<td style="text-align: left;" rowspan="2"><span style="color: #27408c;"><b class="bf">Exponential functions</b></span></td>
<td style="text-align: left;">Formula</td>
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<td style="text-align: left;">Euler's constant</td>
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<td style="text-align: left;" rowspan="2"><span style="color: #27408c;"><b class="bf">Logarithms</b></span></td>
<td style="text-align: left;">Natural logarithm</td>
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<td style="text-align: left;">Exponential and logarithmic differentiation</td>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Unit 3: Approximations</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Released: 7 August</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Due: 9 October</h4>
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<td style="text-align: left;" rowspan="3"><span style="color: #27408c;"><b class="bf">Measurement error</b></span></td>
<td style="text-align: left;">Linear approximations</td>
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<td style="text-align: left;">Sensitivity to error</td>
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<td style="text-align: left;">Combining approximations</td>
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<td style="text-align: left;" rowspan="3"><span style="color: #27408c;"><b class="bf">Quadratic approximations</b></span></td>
<td style="text-align: left;">Best fit parabola</td>
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<td style="text-align: left;">Big “O" notation</td>
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<td style="text-align: left;">Understanding error</td>
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<td style="text-align: left;" rowspan="2"><span style="color: #27408c;"><b class="bf">Newton's method</b></span></td>
<td style="text-align: left;">Algorithm</td>
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<td style="text-align: left;">Why it works, how it can fail</td>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Unit 4: Applications</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Released: 7 August</h4>
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<h4 onclick="hideshow(this);" style="margin: 0px;">Due: 30 October</h4>
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<td style="text-align: left;" rowspan="4"><span style="color: #27408c;"><b class="bf">Graphing and critical points</b></span></td>
<td style="text-align: left;">First derivative test</td>
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<td style="text-align: left;">Second derivative test</td>
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<td style="text-align: left;">Relative max and min</td>
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<td style="text-align: left;">Inflection points</td>
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<td style="text-align: left;" rowspan="3"><span style="color: #27408c;"><b class="bf">Asymptotes and limiting behavior</b></span></td>
<td style="text-align: left;">L'hôpital's rule</td>
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<td style="text-align: left;">Asymptotic behavior</td>
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<td style="text-align: left;">Sketching functions</td>
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<td style="text-align: left;" rowspan="2"><span style="color: #27408c;"><b class="bf">Optimization</b></span></td>
<td style="text-align: left;">Max min problems</td>
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<td style="text-align: left;">Checking end points</td>
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<td style="text-align: left;" rowspan="2"><span style="color: #27408c;"><b class="bf">Related rates</b></span></td>
<td style="text-align: left;">Apply implicit differentiation</td>
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<td style="text-align: left;">Methods of problem solving</td>
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<td style="text-align: left;" colspan="2"><a>Show</a></td>
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